We introduce an anisotropic model of electrostatic interaction based on topological atoms obtained from the gradient vector field partitioning of the electron density. High-order electrostatic moments are computed within the compact spherical tensor formalism from ab initio wave functions of rigid geometry-optimized monomers. When combined with a simple hard-sphere or Lennard-Jones potential this topological electrostatic interaction potential correctly predicts the geometries of 27 DNA base-pairs. With the Lennard-Jones(LJ) potential internuclear distances of frontier atoms between base-pairs differ only by 0.08 Å compared to supermolecular calculations at B3LYP/6-31G(d,p) level. The discrepancy for angles involved in hydrogen bond contacts amounts to only 3.5°. The topological model globally reproduces the correct ranking in intermolecular interaction energy (6.5 ± 6.5 kJ mol-1). Subsequently we compare the interaction energy profiles of the topological model with distributed multipole analysis, Merz-Kollman charges and the natural population analysis at the B3LYP/6-311+G(2d,p) level. The convergence of the topological multipole expansion is somewhat more favorable than that based on DMA but the two models have similar basis set dependence. This work encourages the development of a topological intermolecular potential, which already predicts a reliable geometry of a DNA tetrad in its present form.